From a knowledge of the voltage distribution in earth formation penetrated by a borehole resulting from imposed current flow in the formation, hydrocarbon saturation of the formation can be determined. Rock matrices are generally nonconductors of electricity. But if the formation is porous and contains fluids, current can be driven through the formation, and the voltage distribution along the borehole measured. The impedance of the formation relates to its ability to impede the flow of current through the formation, and is measured in ohms. The resistivity of the formation also relates to the ability of the former to impede current flow but is measured not in ohms but in terms of ohm meter.sup.2 per meter or ohm-meter. That is to say, the resistivity of a formation is the impedance (in ohms) of a one meter by one meter by one meter cube of the formation when the current flows between opposite faces of the cube. Resistivities fall in the range from 0.2 to 1000 ohm-meter in most permeable earth formations we are familiar with.
Since the formation to be logged is penetrated by a borehole containing a fluid having a resistivity other than that of the adjacent formation, the obtained apparent resistivity (Ra) can differ from the true resistivity (Rt) of the formation. That is to say, the presence of the borehole filled with a fluid having a resistivity Rm different from that of the formation, the fact that the drilling fluid filtrate invades the formation to a limited degree and flushes away formation water and some hydrocarbons to establish a resistivity Rxo again different from that of the formation; and the fact that the measuring electrodes may cross into adjacent formations, all perturb the final results.
Certain electrical logging methods overcome such perturbations because of novel borehole conditions. For example, conventional resistivity logs (non-focused logs), provided by conventional electrical survey (ES) tools, provide good true resistivity estimates only in thick homogeneous beds having porosities greater than 15 percent. For thinner bed conditions, such tools can provide reliable results if filtrate invasion is shallow, if the true resistivity is low to moderate and if the resistivity of flushed zone is equal to or less than the true resistivity to be measured.
Additional more advanced logs have been developed to concentrate on enhancing the focusing properties of the electrical tools to overcome the above-mentioned perturbations. For example, families of resistivity tools have been developed in the last quarter century which use focusing currents to control the paths taken by the measuring current: among such tools, are the focusing logging tools including the spherically focused tool. Such tools use currents supplied to special electrodes on the tools and their readings are less affected by borehole conditions and the presence of adjacent beds.
But to an essential degree both types of logs have not been flexible enough under the varying borehole conditions encountered in today's production fields, on land or at sea. For example, conventional ES logs are too broadly structured to provide a way for a user to determine focusing response of electrical tools independent of electrode arrangement. Conversely, focused electrical logs are too strictly formulated to provide such independent results. That is, insufficient measurements are provided to yield results of focusing characteristics beyond that of the original configuration. In addition, calibration factors for deep and shallow focused tools appear to be chosen so that their responses are equal to the true formation resistivity in uninvaded formations having formation/mud resistivity contrasts in a range of 10/1 to 100/1 normalized to an eight-inch borehole. Hence in order for the user to have the option to test different focusing responses independent of electrode arrangement, he had to develop an entirely different logging method.
One such proposal is set forth in U.S. Pat. No. 3,076,138 for "Electrical Logging", R. B. Stelzer in which a multiple electrode array tool is used to provide voltage and current measurements that can be arranged in matrix format within a digital computer, as a function of depth along the borehole.
In the patent, the genesis of the matrix format is described in terms of a 2.times.3 array divided into six submatrices, one of which is a square array whose entries are surprisingly found to be independent of any later electrode arrangement to be synthesized. The above-mentioned square submatrix has rows which can be filled with raw field data values e.g., to identify the voltage at a common depth position and columns of values that can identify voltage responses at a series of voltage electrodes (including the current emitting electrode), as a function of common current electrode location.
It is believed that this proposal is the first to recognize that electrode logging data (viz., current, resistance and voltage) could be combined in such a matrix format.
In field operations, a bottom mounted current electrode is continuously energized as the sonde is moved through the borehole. Absolute voltage measurements at each of the series of uphole pickup electrodes (including the current emitting electrode) are sensed and recorded with respect to a remote uphole voltage reference electrode. A return current electrode is also mounted on the bridle of the tool, suitably located from the other electrodes, and the current from the emitting electrode is also measured and recorded. By dividing the measured absolute voltages by the corresponding measured current in accordance with Ohm's Law in matrix format, a resistance matrix R between arbitrary synthetic voltage and current values can be established. (Henceforth, matrix quantities will be underscored.) In principle, such a resistance matrix is suitable for synthesizing substantially the responses of conventional electric logging tools by manipulation of the matrix elements. Such operations specifically involve a submatrix as explained in more detail below, and is most important in the effectuation of the scheme in accordance with the proposal because of its basic property of allowing the synthetic currents to be uniquely determined from the corresponding voltage, or vice versa.
Also of importance in the practical implementation of the proposal is the recognition that it will generally be necessary to solve systems of equations involving the aforementioned submatrix, or what is equivalent to accurately computing the mathematical inverse of the submatrix to simulate responses of modern focused tools. That is to say, the solution of the reciprocal of such submatrix will be generally necessary for the synthesis of modern focused tools and especially for the synthesis of new and heretofore unknown electrode combinations requiring arbitrary voltage-current relationships. Thus, the above proposal is applicable only to those situations for which it is possible to produce the inverse of the submatrix with sufficient accuracy. But experience has indicated that in many field applications such results are not possible. The problem has to do with the numerical constraints imposed by the measurement process which ultimately result in finite limited precision of the voltage measurements, and has appeared with regularity in those field situations for which the formation to mud resistivity contrast is greater than 100 to 1 (viz., in situations where salty drilling fluids are used; where the uninvaded formation is of low porosity; and where there is moderate to high hydrocarbon saturation). It is believed the failure of the proposal to provide accurate results, has to do with the fact that in such high contrasts, the potential tends to change very slowly from electrode to electrode. Thus it has been impossible to preserve the required precision to accurately resolve the gradual variation involved. As a consequence, in subsequently manipulating matrix potential values, such as where floating point calculations specify differences in the potential between adjacent electrodes, the method of the proposal breaks down.
More recently, a second proposal has been put forth in U.S. Pat. No. 4,087,741 for "Downhole Geoelectric Remote Sensing Method", I. R. Mufti, in which a multiple electrode array tool is described for the detection of lateral resistive anomalies remote from the borehole. Typically, such anomalies are salt domes. This system uses the superposition principle to achieve synthesis of various four (4) electrode tools in the manner of extremely ultra long spaced electric logging tools (ULSEL)--see R. J. RUNGE ET AL, "Ultra-long Spaced Electric Log (ULSEL)", THE LOG ANALYST, Vol. 10, No. 5, September-October, 1969.
More specifically in this proposal, a center mounted current electrode array (viz., a current electrode with voltage sensing electrodes disposed symmetrically above and below the current electrode) is disposed on a bridle of ultra-long length. The current electrode is continuously energized at a low frequency as the bridle is moved through the borehole. Voltage differences between adjacent sensing electrodes above and below the current electrode are measured and recorded. The exclusive purpose of the tool: to synthesize various long-range, four-electrode tools for the detection of lateral anomolies. Since the voltage sensing electrodes are nonuniformly spaced, and since quantities related to the driving point resistance (i.e., the driving point impedance at the current emitting electrodes) are not measured, the proposal does not result in the type of matrix formulation provided by either the first-mentioned proposal or that provided by the present invention. That is to say, while the second proposal will allow calculations of potentials at given electrodes in presence of certain arbitrary currents at other electrodes, it will not allow the inverse calculations, i.e., the calculation of current at a given electrode position for given potentials at other electrode positions via a measured impedance matrix. It therefore cannot be used either in principle or in practice to synthesize other types of logging tools of interest in general.